Biopharmaceutics

PharmaceuticsPHM224Y/PHC330Y

Gregory Poon, Ph.D., R.Ph.

Biopharmaceutics

• Study of delivery of a drug to its intended site of action at the required rate and concentration

• Complex interplay of …• Physicochemical properties of the drug,• Dosage from,• Route of administration, and• Patho(physiology)

on the rate and extent of drug absorption

Biopharmaceutics

• Primary areas of focus • Rate of drug release/dissolution• Rate and extent of absorption

• Except for IV, all routes involve absorption of drug from site of administration

• Rate and extent of first-pass metabolism• Pharmacokinetics is a key set of parameters of a particular

dosage form of a drug, i.e.,• What is the time-dependent concentration of the drug at

a site after administering a particular dosage form?• Generally, we monitor blood concentrations

But why blood concentrations?

• Biological response is function of [drug] at site of action (dose-response curve)

• How to measure the latter in vivo?• Feasible ($)? Possible?

• In some cases, we can monitor the pharmacological response directly• Coagulation (warfarin, heparins, etc.)• BP, HR, etc. (antihypertensives, antiarrhymics, etc.)

• More often we use [drug] in blood as surrogate indicator of drug action• Also basis of therapeutic drug monitoring (TDM)

Blood

Plasma

Serum

Cells

Platelets, clotting factors

Dissolved ions, small molecules,

proteins

Review: separation of whole blood

Learning kinetics is useful!

• Chemical reactions• Drug metabolism

• Noncovalent transitions• Conformational transitions of proteins, DNA, etc.

• Movement between body compartments• Excretion of drug from blood to urine• Diffusion of gaseous anesthetic through alveoli

• Sterilization• Shelf life• Decay of radiopharmaceuticals• Once you’ve understood/modeled the mechanism, the

mathematics are all the same!

Basic kinetics review

• General form of a rate law for a reaction or transition involving n species

• k = rate constant• The reaction is y1

th order wrt X1, y2th order wrt X2, etc.

• yi = 0 (zeroth order; ν independent of [Xi])• yi = 1 (first order)• yi = 2 (second order), etc.

• The overall reaction order is

1 1 2 2 i

1

(productX X ...

[X

) sX

] i

kin

yi

i

y y y

kυ=

+ + + ⎯⎯→

= ∏

1

n

ii

y=∑

More kinetics review

• Rate law cannot be derived from stoichiometry of the balanced equation of a complex mechanism

• However for each elementary step yi does correspond to the stoichiometric coefficient

• In pharmacokinetics, we consider the movement and metabolism of a drug as elementary steps

• We assume that these steps are first-order

Dbloodrk⎯⎯→mk←⎯⎯ DurineMblood

bloodblood blood

[D ] ( )[D ] [D ]r m eld k k k

dtυ = − = + =

A Bk⎯⎯→

[A] [B

[A]( )

] A

?

[ ]d d kdt dt

t

− =

=

=

Properties of first-order reactions

The derivative is proportional to the function itself:what function has this property?

[A] [A]d kdt

= − Remember [A] = ƒ(t)

0

0

ƒ '( ) ƒ( )( ) ( )

[A]( ) ( )[A]

ln[A] ln[A]

cxcx

ct

kt

t C td le c le

dx

t c lee

kt

−

= ⋅

=

=

=

= −

l, c are constants

C is a constant

How much time does it take for A to decay by a fraction ℑ?

0 0

0.9

½

5ln 2

0

ln [A] ln[A]ln

ln

ln 0.9

ln 2

[A] 0.03125[A]

ktkt

tk

tk

tk

e

ℑ

ℑ

ℑ

−

ℑ = −ℑ = −

ℑ= −

= −

=

= =

Half-life

Ex: shelf life of a drug

After 5 half-lives

For first-order reactions, t½ is independent of concentration

Monoexponential decay corresponds to a one compartment model

A two compartment model

Volume of distribution

• A formal quantity, using blood volume as a reference to estimate drug distribution to tissues

Drug Vd (L/Kg) Vd (L, 70 kg)Sulfisoxazole 0.16 11.2 Phenytoin 0.63 44.1 Phenobarbital 0.55 38.5 Diazepam 2.4 168 Digoxin 7 490

Vd: Relationship to physiologic volumes

For 70 kg male

No seriously, where is all the drug hiding?

Area Under the Curve

• Another formal parameter

• 0 < a < t; t + Δt < b < ∞• If c(t) follows monoexponential decay

AUC ( )b

a ba

c t dt− = ∫

0

0DoseAUC p

d el el

cV k k−∞ = =

a b

Determining AUC empirically: trapezoid rule

The trapezoid rule is extremely crude as numerical analysis goes, but it’s only one that’s manually feasible

Non-IV routes involve an absorption phase

• Amount in GI tract

• Amount in plasma

• Even without solving the PDEwe’d expect a modalconcentration-time curvelike this:

Solving the PDEs

Effect of change in ka or F

Minimum Effective Conc.

MaximumSafe Conc.

tmax

cmax

t0Δt

Therapeutic index

Concentration-time curves: vocabulary

Okay this is correct now

Bioavailability

• Official definition (Shargel and Yu, 1995)• Rate and extent of active ingredient reaching systemic

circulation• Operational definition

• Fraction of a given administered dose that appears in systemic circulation

• Fraction absorbed × (1 – fraction metabolized)• AUC used to compare dosage form/route to IV (F = 1 by

definition)

unk

IV

AUCFAUC

=

Bioequivalence

• Two dosage forms of the same drug are bioequivalent if they have the same (relative) bioavailability• New vs. old formulation• Generic vs. brand name

• “Sameness” is a statistical measure• Ex: 90% CI

• AUC is again used as comparator

• Depending on dosage form and application, other parameters are also compared• tmax, cmax

test

ref

AUCFAUC

=

Multiple dosing regimes

• It’s true: we take some drugs more than once• Our assumptions

• One compartment model• Absorption/elimination parameters do not change

• ka, kel, F• Aim = quickly achieve and maintain desired steady state

• MEC < cp < MSC• Get it up, and keep it up

• Only two adjustable parameters• Dose (D)• Dosing interval (τ)

Multiple dosing: summary

• Average ss level determined by D, τ, and ka, and kel

• But ss peak and trough is determined by D only

• Implication for drugs with narrow therapeutic range• Time to ss depends on intrinsic kinetics only!

• Independent of D or τ• css will be different

• Limitations: many drugs exhibit saturable kinetics• Elimination becomes zero-order at high concentrations• Ex: Michaelis-Menten enzyme kinetics

max min

ƒ( , ,{ })ƒ( )

ss

ss ss

c D kc c D

τ=

− =

Physiology of drug absorption from GI tract

The small intestinal epithelium is highly folded

×3×10

×20

Molecular mechanisms of drug absorption

• Epithelial membrane is primary barrier GI content• Apical membrane on brush border

• Basolateral membrane• Transport occurs by

• Diffusion• Carrier-mediated (passive or active)• Pinocytosis (bulk transport)

Diffusion

• To first approximation, assume GI barrier is monolithic• Drug partitions (K1) from lumen into GI barrier, then

partitions (K2) into blood

• K always defined as [D]organic/[D]aqueous

• If drug is highly lipophilic (K >> 0) it partitions in membrane• If drug is highly polar or charged (K ~ 0) it remains in

lumen• How do we quantitatively describe this model?

Lumen GI barrier BloodK1 K2

Fick’s laws: introduction

• Describe flux J of matter across medium• Fick’s first law

• Describes steady state transportbehaviour

• D = diffusion coefficient [L2 t-1]• Fick’s second law

• “Nature abhors a wrinkle”

cJ Dx∂

= −∂

2

2

c cDt x

∂ ∂=

∂ ∂

Fick’s laws are widely applicable

• Drug movement across membranes• Dissolution of solid dosage forms• Gaseous anesthetics across alveoli• Transdermal movement of topically administered drugs• Ion movement in porous soil / concrete

• Geology, civil engineering• Doped ions in semiconductors

• Electrical engineering• Electrophoresis• Non-Fickian diffusion exists, but we’ll leave that to material

scientists

• Let’s assume [Dlumen] and [Dblood] independent of t (steady state)

• Fick’s first law describes flux across GI barrier of surface area A

Applying Fick’s law

1 lumen 2 blood( [D ] [D ])dc DA K KJ Ddx h

−= − =

lumen

h

blood

Mechanistic basis of first-order kinetics

• Now further assume that• K1 ~ K2 ≡ K (lumen and blood essentially aqueous)• [Dlumen] >> [Dblood] ~ 0 (sink conditions)

• First-order kinetics describes (simplified) diffusion kinetics!• Conversely if first-order kinetics is observed at all [Dlumen],

diffusion is predominant transport mechanism

lumen lumen[D ] [D ]DAKJ Ph

= =

Carrier-mediated transport

• Transmembrane protein carriers

Carrier-mediated transport: kinetic properties

• Saturability ensures deviation from first-order behaviour at high [Dlumen]

• Can use Michaelis-Menten equation to model kinetics

• Km and Vmax are intrinsic properties of carrier for given substrate (drug)

max lumen

lumen

[D ][D ]m

VJK

=+

maxlumen[D ]

m

VJK

= maxJ V=

[Dlumen] << Km [Dlumen] >> Km

Carrier mediated transport: energetics

• Energy (ATP) requirement• Active transport (against concentration gradient)

• Ex: riboflavin• Facilitated diffusion (along concentration gradient)

• More often facilitated diffusion is coupled cotransport• Indirectly ATP-burning• Symport or antiport• Popular cosubstrates

• Na+

• Glu, Gal• Di- / tripeptides• Acidic & neutral AAs

• H+

• Sucrose

S-A relationships in carrier-mediated transport

• Drugs that bear structural similarity to endogenous transporter substrate can often “hitch a ride”• Different Km, Vmax

Glucosamine Ceftriazone

Ramipril

Phagocytosis / Pinocytosis

• Bulk transport, often receptor-mediated• Material does not need to be dissolved

• Important for influx ofmacromolecules

• Contents oftenmetabolized inacidic vesicle

Physiological factors affecting bioavailability

• pH• Food (quantity, type)• Gastric emptying rate (GER)• Intestinal motility• First-pass metabolism

• Liver• Intestinal

• Intestinal efflux• P-glycoprotein (pgp)

• Ex: quinine, digoxin• You’ll cover most of these in PHM222Y, but we’ll go nuts

with pH• Most amenable to control in dosage form design

pH along GI tract

• Stomach• pH 1 to 3.5• Increases in presence of food• More acidic at night

• Small intestine• Duodenum pH 5 to 6• Lower ileum pH 8

• Large intestine• pH ~ 8

Ionization and absorption

• Presence of charge impedes partitioning into GI membrane• If drug is ionizable, presence of charge is pH-dependent

• Acid = uncharged at low pH• Base = uncharged at high pH

• Neutral molecules are well absorbed if not too polar• Drugs with permanent charges are often poorly or not at all

absorbed• Ex: quaternary ammonium

• Do you remember what anacid and a base is?

ipratropium

Acid-base definitions

• Brønsted-Lowry: proton transfer• Lewis: electron transfer• For our purposes, life occurs in aqueous environments

• ∴Proton transfers in water• A limited, operational definition

• Acid is a species/functional group that donates proton and becomes ionized

• Base is a species/functional group that accepts proton and becomes ionized

• Requires knowledge of chemistry of substance!• CanNOT be deduced only on the basis of its pKa!!!!!!

C CO

OH

HH

H

C CO

O

HH

H

Some acids

folic acid

Some bases

C NH2

CH2OHCH2OH

CH2OH

Tris

HCl

H2SO4

NaOH

NH4OHglucosamine Gentamicin

Some basic organic chemistry people like to forget

• Common acidic groups• Carboxylic acid (pKa 2-5)• Phenols (pKa ≈ 9)• Thiols (pKa ≈ 8)• α hydrogens

• Aliphatic alcohols are NOT acidic (pKa > 15)• MeOH, EtOH, etc.

• Some transition metals• Mn2+, Fe2+, etc.

• Nonmetal oxides (acid anhydrides)• CO2, SO3

• Common basic groups• Aliphatic amines (pKa 9-12)• Aromatic amines are much

weaker bases (pKa ∼ 5)• Amides are polar but NOT basic• Nitrogens in aromatic systems

(heterocycles) are often very weak bases or not at all

• Metal oxides (base anhydrides)• FeO, CaO, MgO, etc.

And some inorganic chemistry you ought to know

An imide,(weakly) acidic!

phenytoinNH:N

imidazole (pKa = 7.0)

N

pyridine (pKa = 5.25)

NH2

aniline (pKa = 4.63)

NH

pyrrole (pKa = 0)

NH

piperidine (pKa = 11.1)

Beispiel

Not every hydroxyl is acidic

And definitely not every nitrogen is basic

CH3 CO

NH2

pKa = 0.63

CH3CH2OH

pKa = 15.9

CO

OH

pKa = 4.2

OH

pKa = 9.89

NH

CCH2

O

CO

NH

O

barbituric acid (pKa = 4.01)

Ascorbate (pKa = 4.17, 11.6)

Brønsted-Lowry theory

+ -3

2+ -

+ -

(H O ) (A )(H O) (HA)

[H ][A ]55.6 [HA][H ][A ]

[HA]

aa aKa a

=

=

Activities!

Taking a(H2O) = 1; not everyone uses this standard state

[H2O] ≈ 56 M

+ -

+-

-

[H ][A ][HA]

[HA][H ][A ]

[A ]pH p log[HA]

a

a

a

K

K

K

=

=

= +

HA H+

A

CH3COOH CH3COO-H+

C NH3+CH2OH

CH2OHCH2OH

C NH2

CH2OHCH2OH

CH2OHH

+

+

+

+

pKa at 25°C

4.75

8.1

Tris base

+ - -3[HA] [H O ], [A ] [OH ]

Henderson-Hasselbalch

pH-partition hypothesis

• Developed by Brodie in 1950’s• For ionizable drugs, absorbed dose is determined by

extent of nonionization at given pH• Ionized fraction = not absorbed

But wait, is it really true?

• Pegs absorption on equilibrium properties, but GI tract is neither static nor closed

• Other factors are more important• Surface area of small intestine• Lipophilicity independent of ionization

• Perfusion ensures constant near-sink conditions against GI tract, so eventually entire dose will exit lumen as unionized drug … if given enough time in small intestine

• More exception than the rule

Pentamidine: pKa1,2 11.4